When I Merge 2 Spheres together How do Get it to smooth all the combined edges?
It's easier to model the junctions in highly symmetrical objects like this than it seems.

Note that the origin of the spheres object never moves from the World origin. All moves are on the mesh, in Edit Mode.


Starting with a 1/4 of a 16-segment, 8-ring sphere, aligned as
shown, and an empty at the origin
Assign a Mirror modifier in X, and an Array modifier, Count 3, with Object Offset based on the Empty, which is rotated in Z by 120 degrees. Check 'Merge' and 'First and Last' in the modifiers.





In Edit Mode, G X move the mesh until the overlap is right for you
Select all the entirely internal faces, (take a peek on the outside of the spheres, make sure there is no selection showing)





Working on the 'original',  delete the entirely internal faces
On the partially internal faces, slide the internal vertices (G G) down their edges, until they meet their counterparts in the modifier-generated mesh. (Everything's symmetrical, you only have to do this half a dozen times)





Once everything is neat and tidy, add a Z dimension to the Mirror modifier.





After making a copy, and applying the modifiers, perhaps tweak. Here, I X> dissolved a few edges to get all quads, and (CtrlV > Smooth Vertex) eased the triple junction
Throw on a Subdivision Surface modifier.